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Focus (optics)

 
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Focus (optics)
 
 
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In geometrical optics
Geometrical optics

As a mathematical study, geometrical optics emerges as a short-wavelength limit for solutions to hyperbolic partial differential equations. For a less mathematical introduction, please see optics....
, a focus, also called an image point, is the point where light rays originating from a point on the object converge . Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle.






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In geometrical optics
Geometrical optics

As a mathematical study, geometrical optics emerges as a short-wavelength limit for solutions to hyperbolic partial differential equations. For a less mathematical introduction, please see optics....
, a focus, also called an image point, is the point where light rays originating from a point on the object converge . Although the focus is conceptually a point, physically the focus has a spatial extent, called the blur circle. This non-ideal focusing may be caused by aberrations
Aberration in optical systems

Aberrations are departures of the performance of an optical system from the predictions of paraxial optics. Aberration leads to blurring of the image produced by an image-forming optical system....
 of the imaging optics. In the absence of significant aberrations, the smallest possible blur circle is the Airy disc
Airy disc

In optics, the Airy disk and Airy pattern are descriptions of the best focused spot of light that a perfect lens with a circular aperture can make, limited by the diffraction of light....
, which is caused by diffraction
Diffraction

Diffraction is normally taken to refer to various phenomena which occur when a wave encounters an obstacle. It is described as the apparent bending of waves around small obstacles and the spreading out of waves past small openings....
 from the optical system's aperture
Aperture

In optics, an aperture is a hole or an opening through which light is admitted. More specifically, the aperture of an optical system is the opening that determines the cone angle of a bundle of ray that come to a focus in the ....
. Aberrations tend to get worse as the aperture diameter increases, while the Airy circle is smallest for large apertures.

An image, or image point or region, is in focus if light from object points is converged almost as much as possible in the image, and out of focus if light is not well converged. The border between these is sometimes defined using a circle of confusion
Circle of confusion

In optics, a circle of confusion is an optical spot caused by a cone of light ray s from a lens not coming to a perfect focus when imaging a point source....
 criterion.

A principal focus or focal point is a special focus:
  • For a lens
    Lens (optics)

    A lens is an optics device with perfect or approximate axial symmetry which transmittance and refraction light, converging or diverging the beam....
    , or a spherical
    Sphere

    A sphere is a symmetrical geometrical object. In non-mathematical usage, the term is used to refer either to a round ball or to its two-dimensional surface....
     or parabolic
    Parabola

    In mathematics, the parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface....
     mirror
    Mirror

    A mirror is an object with one surface polished, which leads to reflection and another opaque. The most familiar type of mirror is the plane mirror, which has a flat surface....
    , it is a point onto which collimated light
    Collimated light

    Collimated light is light whose ray are nearly parallel, and therefore will spread slowly as it propagates. The word is derived from "collinear" and implies light that does not disperse with distance , or that will disperse minimally ....
     parallel to the axis is focused. Since light can pass through a lens in either direction, a lens has two focal points—one on each side. The distance in air from the lens or mirror's principal plane to the focus is called the focal length
    Focal length

    The focal length of an optics system is a measure of how strongly it converges or diverges light. A system with a shorter focal length has greater optical power than one with a long focal length....
    .
  • Elliptical
    Ellipse

    In mathematics, an ellipse is the apparent shape of a circle viewed obliquely from outside it, as distinct from a hyperbola which is the shape seen from inside....
     mirrors have two focal points: light that passes through one of these before striking the mirror is reflected such that it passes through the other.
  • The focus of a hyperbolic
    Hyperbola

    In mathematics a hyperbola is a smooth function planar curve having two connected components or branches, each a mirror image of the other and resembling two infinite bow aimed at each other....
     mirror is either of two points which have the property that light from one is reflected as if it came from the other.


Glasses 800 Edit
A diverging (negative) lens, or a convex mirror does not focus a collimated beam to a point. Instead, the focus is the point from which the light appears to be emanating, after it travels through the lens or reflects from the mirror. A convex parabolic mirror will reflect a beam of collimated light to make it appear as if it were radiating from the focal point or conversely, reflect rays directed toward the focus
Focus (geometry)

In geometry, the foci, , are a pair of special points used in describing conic sections. The four types of conic sections are the circle, parabola, ellipse, and hyperbola....
 as a collimated beam. A convex elliptical
Ellipse

In mathematics, an ellipse is the apparent shape of a circle viewed obliquely from outside it, as distinct from a hyperbola which is the shape seen from inside....
 mirror will reflect light directed towards one focus as if it were radiating from the other focus, both of which are behind the mirror. A convex hyperbolic
Hyperbola

In mathematics a hyperbola is a smooth function planar curve having two connected components or branches, each a mirror image of the other and resembling two infinite bow aimed at each other....
 mirror will reflect rays emanating from the focal point
Focus (geometry)

In geometry, the foci, , are a pair of special points used in describing conic sections. The four types of conic sections are the circle, parabola, ellipse, and hyperbola....
 in front of the mirror as if they were emanating from the focal point behind the mirror. Conversely, it can focus rays directed at the focal point that is behind the mirror towards the focal point that is front of the mirror as in a Cassegrain
Cassegrain reflector

The Cassegrain reflector is a is a combination of a primary concave mirror and a secondary convex mirror, often used in optical telescopes and Antenna s....
 telescope
Telescope

A telescope is an instrument designed for the observation of remote objects by the collection of electromagnetic radiation. The first known practically functioning telescopes were invented in the Netherlands at the beginning of the 17th century....
.

See also

  • Cardinal point (optics)
    Cardinal point (optics)

    The cardinal points and the associated cardinal planes are a set of special Point s and Plane s in an optics system, which help in the analysis of its paraxial approximation properties....
  • Defocus aberration
    Defocus aberration

    In optics, defocus is the one aberration in optical systems familiar to nearly everyone who has ever needed eyeglasses or used a camera, videocamera, microscope, telescope, or binoculars, as it simply means out of focus ....
  • Depth of field
    Depth of field

    In optics, particularly as it relates to film and photography, the depth of field is the portion of a scene that appears sharp in the image. Although a lens can precisely focus at only one distance, the decrease in sharpness is gradual on either side of the focused distance, so that within the DOF, the unsharpness is imperceptible under nor...
  • Depth of focus
    Depth of focus

    Depth of focus is a Lens optics concept that measures the tolerance of placement of the image plane in relation to the lens. In a camera, depth of focus indicates the tolerance of the film's displacement within the camera, and is therefore sometimes referred to as "lens-to-film tolerance."...
  • Far point
    Far point

    In visual perception, the far point is the point at which an object must be placed along the optical axis for its image to be focused on the retina when the eye is not accommodation reflex....
  • Focus (geometry)
    Focus (geometry)

    In geometry, the foci, , are a pair of special points used in describing conic sections. The four types of conic sections are the circle, parabola, ellipse, and hyperbola....
  • Fixed focus
  • Bokeh
    Bokeh

    Bokeh is a photographic term referring to the appearance of out-of-focus areas in an image produced by a camera photographic lens using a shallow depth of field....